Sibling Spillovers

Take three siblings equally spaced in age. Here’s an advantage the second child has over the third.

When the oldest learns something new, the second will have a chance to learn a little of it alongside. For example, say the parents are teaching the oldest algebra in the car while on vacation (dreadful parents for sure.) All three siblings will be listening but the second, being older than the youngest is going to grasp more of it.

Now when the second reaches the same age that the oldest was at the time of the algebra lesson, the second will be more advanced than the oldest was as a result of the spillovers from the original lesson. The parents will know this and they will appropriately scale up the lesson. It will go faster and it will be more advanced. As a result the lesson will be less accessible to the youngest child than the original lesson to the oldest was to the second. The third child will benefit less from the spillovers than the second child did.

This process implies that the human capital of the second will closely track the oldest and diverge from the youngest so that parental investments tailored to the current human capital level of the oldest will have benefit the second more than the youngest by an ever increasing differential. And investments tailored to the level of the second will be too advanced to benefit the youngest.

Now the original assumption was that the siblings are equally spaced in age. Suppose instead that the two youngest are close in age and the oldest is much older. Then there will be little scope for spillovers from the oldest to the second. The second will have to be taught everything from scratch and now the youngest is going to receive the only spillovers. So the larger gap in age between the oldest and the second the smaller the advantage of the second over the third. And for a large enough gap the advantage reverses.

One of the underlying assumptions is that the learning goes from the parents to the children – i.e., that siblings don’t teach each other, or that they teach each other little enough that those effects can be ignored. That’s where I’d question the model, especially given both personal history and observations of every group of siblings I’ve ever known.

Adding in those effects, the youngest still gets more and more benefit (on average), because s/he gains even more teachers who are helping him/her navigate the particular contexts of that family, and who can provide exemplars of what to do or not to do.

There’s also the case where the first two children are significantly older than the third, which can lead to the first two then treating the youngest like a child they’re babysitting/responsible for themselves (i.e., the sibling-as-teacher effect becomes more pronounced). Further, that youngest can then also experience significant time as an “only child,” gaining the attention of the parents plus the benefits of their experience as parents.

why would the parents myopically optimize for the second child (targeting lessons for him/her in particular), rather than taking into account the externalities described and maximizing the sum of child learning?